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Lanthanum Zirconate Based Thermal Barrier Coatings: A Review
Jing Zhang a,*,Xingye Guoa, Yeon-Gil Jung b, Li Lic, James Knapp c
a Department of Mechanical Engineering, Indiana University-Purdue University Indianapolis, Indianapolis, IN 46202, USA
b School of Materials Science and Engineering, Changwon National University, Changwon, Gyeongnam 641-773, Republic of Korea
c Praxair Surface Technologies Inc., Indianapolis, IN 46222, USA
*Corresponding author: [email protected]
Abstract
This review article summarizes the latest information about the manufacturing techniques
of lanthanum zirconate (La2Zr2O7, LZ) powder and La2Zr2O7 based thermal barrier coatings
(TBCs). Lanthanum zirconate is a promising candidate material for TBC applications, due to
its lower thermal conductivity and higher thermal stability compared to other traditional TBC
systems. In this work, the physical, thermal, and mechanical properties of the powder and
coatings are evaluated. The durability experiments of the TBCs in various thermal,
mechanical, and corrosive conditions is also reviewed. In addition, theoretical studies on the
powder and coatings properties are presented. Finally, future research directions of lanthanum
zirconate as TBC applications are proposed.
Keywords: Lanthanum zirconate; Thermal barrier coating; Properties; Durability;
Modeling
_________________________________________________________________________________ This is the author's manuscript of the article published in final edited form as:
Zhang, J., Guo, X., Jung, Y.-G., Li, L., & Knapp, J. (2016). Lanthanum zirconate based thermal barrier coatings: A review. Surface and Coatings Technology. https://doi.org/10.1016/j.surfcoat.2016.10.019
2
1 Introduction
Thermal barrier coatings are multi-layer coating systems deposited on turbine components,
especially turbine blade, which thermally insulate and protect them against hot and corrosive
gas streams [1-3]. Typical structure of TBCs includes four layers: (1) superalloy substrate; (2)
bond coat; (3) thermally grown oxide (TGO); and (4) ceramic top coat. The bond coat consists
of a MCrAlM’ intermetallic alloy with a thickness of 100 ~ 300 μm, wherein M is an element
selected from nickel, cobalt, iron and their mixture, and M’ is an element selected from
yttrium, zirconium, hafnium, ytterbium and mixture thereof [4]. Typically, TBCs can be
deposited directly on the substrate using various techniques, such as air plasma spraying
(APS), electron-beam physical vapor deposition (EB-PVD), high velocity oxygen-fuel
(HVOF) spraying, vacuum plasma spraying, low-pressure plasma spraying and diffusion
bond method [5-8]. In high-temperature operation conditions, a TGO layer is formed at the
interface between the bond and top coats with a thickness of 1~10 μm. The main composition
of TGO is α-alumina (α-Al2O3), which functions as a good oxygen diffusion barrier. The
ceramic top coat is one or multiple low thermal conductivity ceramic layers with a typical
thickness of 100 ~ 600 μm, which is deposited by APS or EB-PVD methods [3, 9]. The criteria
for selecting TBC materials include high melting point, low thermal conductivity, high
coefficient of thermal expansion (CTE), good thermal and chemical stability, no phase change,
low sintering activity, good erosion resistance, and good foreign objective damage (FOD) or
calcium–magnesium–alumino-silicate (CMAS) resistance [10].
Currently, the state-of-the-art TBCs are 7~8 wt % yttria stabilized zirconia (8YSZ). 8YSZ
has a metastable tetragonal phase (t’), and Y2O3 is used to stabilize the ZrO2 structure. 8YSZ
has a relatively high melting point (2680 oC) [10], relatively low thermal conductivity ( 2.0–
2.3 W/m/K at ~1000 oC for a fully dense; 0.9–1.2 W/m/K for 10–15 % porosity) [11, 12], a
relatively high CTE (11×10-6 /K at ~1000 oC) [10], and good thermal and chemical stability
[13]. However, the maximum surface temperature that can be employed for 8YSZ based
TBCs is limited to 1200 oC for long term operations. At temperatures above 1200 oC, there
are two important degradation mechanisms in 8YSZ. The first mechanism is that the t’ phase
of YSZ will decompose into two equilibrium tetragonal (t) and cubic (c) phases. During
cooling process, the t phase will transform to the monoclinic (m) phase, accompanied with
~4% volume expansion. The other mechanism is the sintering of coating, which will densify
3
the microstructure, and thus increase the thermal conductivity. The phase and microstructure
changes as well as property changes will finally lead to high thermal induced stress and
reduced coating’s lifetime [10] [14]. Therefore, there is continued effort searching for
alternative TBC materials that meet the needs of next-generation advanced gas turbines.
Lanthanum zirconate (La2Zr2O7, LZ) is a typical pyrochlore structure ceramic material.
The general chemical formula of the pyrochlore structure is A2B2O7. A element in A2B2O7
generally is a rare earth or an element with an inert single pair of electrons, and B element
typically is a transition metal or a post-transition metal with a variable oxidation state [5, 15].
Compared to 8YSZ, LZ has many advantages for TBC applications: (1) no phase
transformation from room temperature to its melting temperature; (2) considerably high
sintering resistance; (3) a very low thermal conductivity (1.5–1.8 W/m/K at 1000 oC for a
fully dense material); and (4) LZ has a lower oxygen ion diffusivity, which protects the bond
coat and the substrate from oxidation [10]. The principle drawback of LZ is its low CTE value,
which does not match the high CTE values of bond coat and substrate.
The objective of this paper is to provide a comprehensive review of the manufacturing
techniques of LZ powder and LZ based thermal barrier coatings, with a focus of comparing
LZ with 8YSZ, the current state of the art thermal barrier coating material. The paper is
arranged as follows. Chapter 2 provides the information of fabrication technique and
characterization of LZ powder. Chapter 3 presents the fabrication methods of LZ based TBCs.
Chapter 4 summarizes the physical properties of LZ based TBCs. Chapter 5 shows coatings’
thermal properties. Chapter 6 presents coatings’ mechanical properties. Chapter 7 provides
the durability analyses, including thermal cycling test, erosion test, hot corrosion, and CMAS
infiltration damage test. Chapter 8 presents modeling and simulation studies. Chapter 9
provides concluding remarks on future research directions.
2 Fabrication and characterization of lanthanum zirconate powder
2.1 Powder fabrication
There are several fabrication methods for LZ powder, including solid state reaction method,
co-precipitation method and sol-gel method, etc. [10, 16-18]. For thermal spray applications,
4
LZ powder can be synthesized by the solid state reaction method from a mixture of the
lanthanum oxide (La2O3, 99.9%) and ZrO2 (99%) powders at high temperatures (1773 K)
under an argon atmosphere for 10 hrs [16, 17]. The pure La2O3 is typically prepared by
dissolving La2(CO3)3·8H2O in nitric acid and subsequently producing a precipitate by addition
of NH3. The precipitate is dried in air and then heated in oxygen at 1173 K to remove the
nitrogen-containing fragments. The resulting La2O3 is heated at 1473 K to remove any
absorbed water [16]. The fabricated LZ powders are in spherical or ellipsoidal shape with a
porous microstructure. The theoretical chemical composition of LZ powder is: La 48.6 wt.%,
Zr 31.9 wt.%, O 19.5 wt.%, which is equivalent to 1:2 molar ratios of La2O3 to ZrO2 [13].
In the co-precipitation method, an aqueous solution of lanthanum nitrate hexahydrate
(La(NO3)3·6H2O) and zirconium oxychloride (ZrOCl2·8H2O) with a diluted NH3 solution is
used to prepare LZ powder [10]. During this preparation process, the La(NO3)3·6H2O and
ZrOCl2·8H2O are dissolved in distilled water in equimolar amounts. The liquid mixtures are
slowly added under stirring to an ammonium hydrate solution with pH 12.5. The resulting
precipitate is filtered, washed with distilled water, and then dried at 120°C overnight. The
remaining solid is then calcined at 900°C for 5 hrs. The sol-gel method is another way to
synthesize nanostructured powders, which have high sintering ability for the A2Zr2O7 (A=La,
Nd, Sm) system [18].
The manufacturing criteria of LZ feedstock powders are (1) spherical shape powder, (2)
uniform and fine particle size, (3) homogeneous composition, (4) high purity, and (5) low
fabrication cost. The requirements of the shape and size distribution are based on the fact that
powder flowability is very important in thermal spray process. The spherical shaped powder
and its uniform particle size are critical for smooth flow of powders through the feedstock-
feeding pipe.
2.2 Crystal structure
LZ is a typical ZrO2-Ln2O3 (Ln is lanthanide elements, Ln= La ~ Gd) system, which has a
pyrochlore structure with a space group 3 [19]. Although the Ln2Zr2O7 (Ln=La ~ Gd)
compounds are stable at room temperature, an order-disorder transition occurs at high
temperatures (>1500 oC), namely the compounds change from pyrochlore to defect fluorite
5
structure, with the only exception of LZ (Ln2Zr2O7, Ln=Tb ~ Lu) which adopts the defect
fluorite structure [15]. The transition temperature depends on the radius of Ln ions (La, no
transition; Nd, 2300 oC, Sm 2000 oC, and Gd 1530 oC) [20].
X-ray diffraction is widely used to identify the crystal structures. Fig. 1 shows the X-ray
diffraction patterns of several Ln2Zr2O7 materials at room temperature [18]. Two peaks, (331)
and (511), shown in the LZ pattern originate from pyrochlore structure, and are also observed
in Nd2Zr2O7, Sm2Zr2O7, and Gd2Zr2O7 patterns. Other peaks are commonly observed for the
pyrochlore and defect fluorite structures [18].
6
Fig. 1: X-ray diffraction patterns of Ln2Zr2O7 [18].
Ln2Zr2O7 pyrochlore crystal is a cubic structure in space group 3 (origin choice 2)
with four crystallographically independent atom sites (rear earth ion Ln, in 16d at ( , , ) ,
Zr in 16c at (0,0,0), O1 in 48f at (x, , ) and O2 in 8b at ( , , ). The structure type can be
considered as an ordered defect fluorite structure with the trivalent rare earth Ln3+ and
quadrivalent Zr4+ cations forming an ordered, ccp eutectic cation array. Oxygen ions are
7
located at of the tetrahedral interstices: O1 in an off-center position within the Ln2Zr2
tetrahedral, O2 in the Zr tetrahedral [21]. The x values of O1 can be varied from 0.3125 to
0.375. The x values 0.3125 and 0.375 correspond to the regular octahedral oxygen
environment around the Zr4+ ion and regular cubic oxygen environment around Ln3+
respectively. Tabira et al. determined the x value of La2Zr2O7 using systematic row wide-
angle convergent beam electron diffraction (CBED) techniques [21]. The results showed that
the x value varied systematically with the rare earth ion radius, the larger radius corresponding
to the larger x value. The experimental result of x value in LZ is 0.333, according to Tabira’s
work [21].
The lattice parameter of a conventional cubic LZ cell can be calculated using XRD results
based on Bragg’s Law. Shimamura et al. reported that the lattice parameters of Ln2Zr2O7
pyrochlores increased with the ionic radius of Ln, as shown in Fig. 2 [18]. The lattice
parameter of LZ is 10.8 Å in Shimamura’s experiments and 10.802 Å in Tabira’s work [21].
Fig. 2: Lattice parameters of Ln2Zr2O7 as a function of ionic radius. Solid and open symbols stand for pyrochlore and defect fluorite structures, respectively [18].
8
2.3 Phase stability
As discussed from the XRD pattern in Fig. 1, LZ has a cubic phase at room temperature.
As shown in the ZrO2-La2O3 phase diagram of Fig. 3, LZ has no phase transformation from
room temperature to its melting point [22-24]. When the molar ratio of ZrO2 and La2O3
becomes 2:1, which corresponds to 33.3% La2O3, only a single LZ cubic phase is available
from room temperature to its melting point.
Fig. 3: Phase diagram of ZrO2 and La2O3 (in mole %) [22-24].
9
In addition, in situ phase stability of LZ from room temperature to 1673K (1400 oC) has
been studied using synchrotron X-ray diffraction (XRD) at Argonne National Laboratory, as
shown in Fig. 4 [25-27]. The results showed that LZ has no phase transformation in the
temperature range of 303–1673 K (30–1400 oC) [25].
Fig. 4: in situ high energy XRD spectrum of LZ in the temperature range of 30 – 1400 oC.
3 Deposition techniques of lanthanum zirconate based TBCs
3.1 Air plasma sprayed coating
APS is the most widely used thermal spray technique for LZ deposition. During APS
process, feedstock powders are carried by noble gasses, such as Ar, to the APS torch. The
thermal plasma is generated using electric arcs. Natural air is used as the source of the plasma
gas for the LZ thermal spray. The essential APS parameters include current, carrier air flow
rate, primary air flow rate, spray distance, powder feed rate, and substrate tangential speed
[28].
0 1 2 3 4 5 6 7 8
Cou
nts
(a.u
.)
2 Theta (deg.)
1400
30
Tem
pera
ture
(o C
)
10
As shown in Fig. 5, APS sprayed LZ coating has many pores and cracks, which is well
known as the “splat” grains [28]. The thermal conductivity of the APS deposited coating is
lower than the one from EB-PVD process, due to its “splat” grain morphology. The porosity
of the LZ coating can be easily controlled by changing the spray parameters, which results in
changing the thermal conductivity and the mechanical properties.
Fig. 5: Cross-sectional view of the microstructure of APS’d LZ TBC [28].
3.2 EB-PVD deposited coating
Another commonly used deposition technology is EB-PVD. The main EB-PVD deposition
parameters include vacuum pressure, substrate distance, power supply, average substrate
temperature (1223 ± 25 K, 950 ± 25 oC) and substrate rotation speed [29, 30]. The overall
porosity of those coatings is similar to APS coatings. The main difference is the arrangement
of the pores, gaps and cracks which creates the differences in thermal conductivity. As shown
in Fig. 6, the EB-PVD deposited LZ coating microstructure has a fine columnar
11
microstructure that results in a higher strain tolerance [31]. Typically, EB-PVD deposited
coating has a higher thermal conductivity than APS sprayed coatings at the same porosity
level. The splat boundaries of APS deposited coatings act as scattering centers, and are
perpendicular to the direction of heat flux. In contrast, the columnar grain boundaries in the
EB-PVD deposited coatings are parallel to the direction of heat flux. As a result of higher
strain tolerance, the EB-PVD deposited coatings have a good performance and considerably
longer operating lifetime [7]. The main disadvantages of the EB-PVD technique are its low
deposition rate, high investment costs, higher thermal conductivity, and vapor pressure
requirements.
Fig. 6: Cross-sectional view of the microstructure of EB-PVD deposited LZ coating [31].
3.3 Other deposition techniques
In addition to the two methods mentioned above, there are other techniques to deposit LZ
coatings, such as suspension plasma spray (SPS) and spray pyrolysis [7, 32, 33].
Wang et al. deposited a LZ coating using the SPS method [32]. A suspension of 30 wt.%
nano-LZ particles in (99.5%) ethanol was produced. Meanwhile, an electrostatic dispersant
of 1 wt.% polyethylene glycol (PEG1000) was added to the suspension. The suspension was
injected into the plasma spray jet and the LZ coating was deposited. The main deposition
12
parameters were standoff distance of the substrate and the concentration of the suspension
feedstock. A liquid solution was used as a feedstock material instead of powder, which
provided the possibility of tailoring the coating composition and the deposition of the doped
multilayered coatings [33]. As shown in Fig. 7a and Fig. 7b, many pores and cracks were
spotted in the microstructure of the SPS deposited coatings [32]. Weber et al. fabricated the
LZ coating using the spray pyrolysis method [33]. Zirconyl oxynitrate hydrate
(ZrO(NO3)2·xH2O) and lanthanum nitrate hexahydrate (La(NO3)3·6H2O) were dissolved in
deionized water and further mixed in a molar ratio of 1:1 of La and Zr. The precursor solution
was sprayed at the flow rate of 1 ml/min at 240 oC. The deposited coatings were dried at
500~600 oC after the deposition process. As shown in Fig. 7c and Fig. 7d, many cracks were
observed in the coating layer [33].
13
Fig. 7: Cross-sectional views of the microstructure of LZ coatings (a) SPS deposited with standoff 40mm, (b) SPS deposited with a standoff 50 mm, and (c) surface view and (d) cross sectional view of spray
pyrolysis deposited LZ coatings [32, 33]
4 Physical properties of lanthanum zirconate based coating
4.1 Coating density and porosity
The theoretical density of LZ material can be calculated using the molecular weight and
the number of formula units per elementary cell [34]. Lehmann et al. calculated the theoretical
density of LZ material to be 6050 kg/m3 [34].
For porous LZ coatings, the density can be measured following the ASTM standard B328-
96, which is based on the Archimedes’ principle [35]. The porosity of the LZ coating varies
with the deposition parameters, such as deposition power, powder feed rate and substrate
standoff distance. For APS deposited coatings, a denser coating would be produced by
increasing the power used in the torch, or increasing powder feed ratio, or reducing standoff
distance. Commercial APS deposited coating shows an average porosity of 15~25 %.
However, it is important to tailor the porosity of the LZ coating in a range of 8~19% to acquire
good thermal and mechanical properties [36].
4.2 Sintering behavior
Sintering of porous ceramic coating is the process in which the coating is densified by the
reduction in surface energy associated with the excess surface area of the pores and cracks
[2]. Sintering of the porous TBCs normally occurs at elevated temperatures. When sintering
occurs, densification process inevitably increases the elastic modulus and thereby decreases
the strain compliance of the coating. Meanwhile the thermal conductivity of the coating
increases due to the decrease of the porosity [2].
Many experimental approaches can be used to quantify the sintering behaviors: 1) measure
the dimensional change of the coating sample using a high-temperature dilatometer; 2)
determine porosity distribution and its change using a mercury porosimetry; 3) measure the
relative density of the coating during the sintering process based on the Archimedes’ principle;
14
4) derive from the measured thermal conductivity changes during long time heating periods
at various temperatures [10, 37, 38]. Vassen et al. investigated the sintering behavior of APS
deposited LZ coating at temperatures as high as 1650 oC using the high-temperature
dilatometer and the mercury porosimetry methods [10, 37]. Higher porosity led to higher
sintering rate. The coating with a porosity of 20% densified substantially during an annealing
process at 1250 oC [37]. Vassen et al. commented that decrease in porosity might lead to a
better thermomechanical behavior [10]. Zhu et al. investigated the sintering behavior by
continuously monitoring the thermal conductivity evolution [38]. Zhu found that the LZ
coating showed a significant thermal conductivity increase (from 0.55 W/m/K to 0.95 W/m/K
in 20 hrs.) at 1575 oC, suggesting the coating was undergoing substantial sintering. Nair et al.
also studied the sintering behavior of LZ coating [39]. They found that the major mechanism
of the sintering process was surface diffusion, in the temperature range of 800–1100 oC.
Sintering above 1100 oC was mainly because of grain boundary diffusion combined with
surface diffusion. The contribution from surface diffusion became negligible as the sintering
temperature increased.
In general, the sintering resistance of LZ coating is higher than that of YSZ coating, and
also BaZrO3 and SiZrO3 coatings [10, 37]. The low-sintering activity of the LZ is beneficial
for TBC applications.
4.3 Crack and pore morphology
The crack and pore morphology of TBCs is a crucial parameter affecting the thermal and
mechanical properties of the coatings. Cracks can be categorized as horizontal, vertical, and
spherical forms. Zhang et al. studied the crack morphology of the APS deposited LZ coating
using a quantitative imaging analysis method [40]. It was found that the cracks were primarily
horizontal in the top and middle regions of the cross section area, while vertical cracks became
dominant in the bottom region. In addition, the calculated porosities showed a non-uniformity
in the cross sectional area.
Weber et al. showed that vertical crack is beneficial in LZ TBC application due to enhanced
thermomechanical compliance [3, 41]. The LZ based TBCs were deposited using the spray
pyrolysis method, and the vertical cracks were introduced by decomposing the metal salt and
15
drying the coating layer at 575 oC, as shown in Fig. 7d. Moreover, the multilayer coating with
vertical cracks was fabricated by the successive deposition and decomposition of multiple thin
layers. Heat conduction was small in this multilayer coating due to the generated cracks, and
the thermal durability can be increased due to the increased thermo-mechanical compliance
[41].
5 Thermal properties of lanthanum zirconate based coating
5.1 Melting point and specific heat capacity
Melting point is an important criterion for selecting TBC materials, which is critical for
the thermal stability in high-temperature operation environments. Thermal analysis is the
commonly used method to detect the melting point, which is performed in sealed tungsten
crucibles, and the sample temperature is monitored by a spectro-pyrometer. In addition, high-
temperature X-ray diffraction experiments, e.g., in Advanced Photon Source at Argonne
National Laboratory, can also be used to determine the melting temperature by monitoring the
pyrochlore (111) peaks [42, 43]. As shown in Table 1, the experimentally measured melting
point of the LZ is approximately 2523–2573 K (2250–2300 oC), which is lower than that of
YSZ (2953 K, 2680 oC) [10, 37, 42]. Although the melting point of LZ is lower than that of
YSZ, it is still sufficiently high for most TBC applications.
Table 1: Thermal properties of La2Zr2O7 coating vs. YSZ coating
LZ YSZ
Melting point 2523–2573 K (Vassen [10, 37], Hong [42]) 2953 K
(Vassen [10])
Specific heat capacity
0.48 J/g/K (@ 1200 K, Vassen [10])
0.41 J/g/K (@ 400 K, Bolech [16])
0.42 J/g/K (@ 400 K, Sedmidubsky [17])
0.44 J/g/K (@ 1200 K, Girolamo [28])
0.65 J/g/K (@ 1200 K, Khor [44])
Thermal conductivity
1.55 W/m/K (dense, @1273 K, Vassen
[10])
2.15 W/m/K (dense, @ 1273 K, Zhu [38])
2.25 W/m/K (dense @1273K,
Vassen [10])
16
0.68 W/m/K (porosity 11.54 %, @ 1173 K,
Guo [45])
0.87 W/m/K (porous, @ 1273 K, Bobzin
[31])
0.88 W/m/K (Porous, @ 1173 K,
Guo [45])
1.38 W/m/K (porous, @ 1273 K,
Bobzin [31])
Coefficient of
thermal expansion
9.45 ×10-6 /K (273–1473 K, Chen [46])
9–10 ×10-6 /K (400–1600 K, Guo [45])
9.0–9.7 ×10-6 /K (400–1600 K, Zhang [47])
7.6–9.1×10-6 /K (400–1400 K, Lehmann
[34])
11×10-6 /K (dense @ 1273 K,
Vassen [10]
Differential scanning calorimetry (DSC) is the most widely used technique to precisely
measure the specific heat capacity (Cp). Several researchers investigated the specific heat
capacity of LZ in different conditions, as shown in Fig. 8 [10, 16, 17, 28, 48, 49]. In Vassen ’s
work, the LZ samples were densified by hot pressing at 1350~1400 oC. LZ samples in powder
form were used in Bolech and Sedmidubsky’s work. In Girolamo’s work, the specific heat of
the LZ coating with a porosity of 11% was measured. The specific heat of 8YSZ is ~ 0.55 -
0.65 J/g/K in the temperature range of 300-1200 oC, which is larger than that of the LZ [44].
For the TBC materials, small Cp values are preferred to reduce thermal diffusivity.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 400 800 1200 1600
Sp
ecif
ic h
eat
(J/g
/K)
Temperature (K)
Exp. by Vassen [10]
Exp. by Bolech [16]
Exp. by Sedmidubsky [17]
Exp. by Girolamo [28]
Calc. by Guo [48]
Calc. by Chartier [49]
17
Fig. 8: Specific heat capacity (Cp) of LZ in the temperature range from 0 ~ 1600 K.[10, 16, 17, 28, 48, 49]. Notice that Guo and Chartier’ s Cp curves are overlapped below 1000 K.
5.2 Thermal conductivity
For TBC materials, thermal conductivity is the most important material property. Thermal
conductivity can be determined using thermal diffusivity, specific heat capacity and density,
which can be independently measured experimentally. The most widely used experimental
method to measure the thermal diffusivity is the laser-flash method. Vassen et al. measured
the thermal conductivity of LZ samples using the laser-flash method, in which samples were
prepared by hot pressing in the temperature range of 1350–1400 oC [10, 34]. The density of
the hot pressed sample was greater than 95%. The thermal conductivity that Vessen measured
was ~ 1.5-2.0 W/m/K in the temperature range of 200-1400 oC. Zhu et al. did similar studies
for the hot pressed disk-shape samples using the spray-dried LZ powders [38, 50]. The
measured thermal conductivities of the densified LZ were 2.0-4.0 W/m/K, which were larger
than Vessen’s results, in the temperature range of 200–1400 oC. The thermal conductivity is
very sensitive to porosity level. A low porosity leads to a high thermal conductivity. The high
thermal conductivity in Zhu’s work may be due to the coating’s lower porosity than that in
Vassen’s work. Guo et al. measured the thermal conductivities of APS deposited LZ coating
with a porosity of 11.54% using the laser-flash method [45]. The measured average thermal
conductivity of the porous LZ was ~ 0.59–0.68 W/m/K in the temperature range of 297 - 1172
K (24–899 oC). Chen et al. also measured the thermal conductivity of APS deposited LZ
coating with a lower porosity [46]. Bobzin et al. investigated the thermal conductivity of
mixed 7 wt.% YSZ and La2Zr2O7 layers deposited by the EB-PVD method [31]. All of the
experimental data and a modeling result [51] (see section 8.1 for thermal conductivity
modeling details) are compiled in Fig. 9.
As shown in Fig. 9, the thermal conductivities of the LZ coating decrease with the increase
of temperature till 1200 K due to lattice scattering, and the conductivities increase again above
1200 K due to radiation contribution. The conductivities also depend on coating porosity [10,
31, 38, 45, 46, 51]. In Vassen and Zhu’s works, the porosities of the LZ samples were very
low so the thermal conductivities were much larger than those of the porous coatings in Guo,
Bobzin and Chen’s research.
18
Fig. 9: Thermal conducitivity of LZ in the temperature range of 273 – 1700 K [10, 31, 38, 45, 46, 51].
In addition to porosity, doped LZ materials were developed to further reduce the thermal
conductivity and improve thermal cycling and mechanical properties. Lanthanide elements
are possible dopants because they form a similar pyrochlore structure with ZrO2. Lehmann et
al. showed that the thermal conductivities of the Nd, Eu, Gd and Dy doped LZ (30% of La3+
was substituted) were lower than that of pure LZ below 1000 oC [34]. Lehmann noted that the
thermal conductivity was affected by the atomic mass and radius of the substituted and
substituting atoms. Bansal et al. suggested that Gd and Yb can replace the La3+ cation to form
new pyrochlore structured materials such as La1.7Yb0.3Zr2O7, La1.7Gd0.3Zr2O7 and
La1.7Gd0.15Yb0.15Zr2O7 [50]. The Gd and Yb doped LZ showed a lower thermal conductivity,
a better high-temperature stability up to 1650 oC and a better sintering resistance than LZ. In
addition, Yb, Ce, Y, In and Sc were reported as dopants for both La3+ and Zr4+ site [52, 53].
Xiang et al. showed that (La0.7Yb0.3)2(Zr0.7Ce0.3)2O7 and (La0.2Yb0.8)2(Zr0.7Ce0.3)2O7 had lower
thermal conductivities than LZ [53]. Wang found that (La1-x1Yx1)2(Zr1-x2Yx2)2O7, (La1-
x1In1x2)2(Zr1-x2Inx2)2O7 and (La1-x1Scx1)2(Zr1-x2Scx2)2O7 had the potential to achieve lower
thermal conductivity than LZ [52].
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 500 1000 1500 2000
Th
erm
al c
ond
uct
ivit
y (W
/m/K
)
Temperature (K)
Exp. by Zhu [38]Exp. by Vassen [10]Exp. by Bobzin [31]Exp. by Guo [45]Exp. by Chen [46]Calc. by Guo [51]
19
Low thermal conductivity is the primary advantage of LZ coatings over the YSZ coatings.
Vassen et al. compared the thermal conductivity of hot pressed YSZ and LZ samples [10].
Vassen noted that high dense LZ samples’ thermal conductivities were 30-35% lower than
YSZ at 800-1000 oC, in the similar porosity level. Bobzin et al. showed that the thermal
conductivity of EB-PVD deposited 7YSZ was about 25-40% higher than the EB-PVD
deposited LZ coating [31]. Guo et al. showed that the thermal conductivity of APS deposited
porous LZ coating was ~25% lower than that of APS deposited porous 8YSZ coating [45].
5.3 Coefficient of thermal expansion
TBC is a multi-layer material system including alloy, intermetallic bond coat, TGO layer
and ceramic top coat, therefore the volume change in the thermal cycling process is different
due to the different CTEs in each layer. Thermally induced residual stress generated among
TBC layers due to CTE mismatch becomes a primary cause of failure [9]. Since the CTE
values of superalloy substrate and bond coat are usually about 15×10-6 and 14×10-6 /K,
respectively, at 1000 oC [4, 9], which are much larger than the typical ceramic top coat. As a
result, large CTEs are preferred for the ceramic top coat to reduce CTE mismatch.
Additionally, due to large thickness of substrate, its CTE influence may be more important
than bond coat.
The most widely used approach to measure CTEs is the dilatometry method. The linear
CTE value can be obtained from the measurement of the temperature-dependent sample
length change using a high-temperature dilatometer. Many researchers measured the CTEs of
LZ using a dilatometer, as summarized in Fig. 10 and Table 1 [34, 45-47, 54]. Chen et al.
investigated the CTEs of both bulk LZ material and APS deposited LZ coating, and the results
showed a similar trend [46]. The apparent CTE value of the LZ coating was about 9.45×10-6
/K in the temperature range of 0 ~ 1200 oC. Guo et al. also measured the CTE of LZ coating.
The average porosity of the APS deposited LZ coating in Guo’s measurement was 11.54 %
[45]. Zhang et al. determined the CTE value of LZ powders by measuring variation of lattice
parameters during heating process [47]. The lattice parameters came from the XRD analysis
at different temperatures. Lehmann, using a dilatometer, investigated the CTE of hot pressed
LZ samples with a relative density between 69 % and 93 % [34].
20
Fig. 10: CTEs of LZ in the temperature range of 273 – 1600 K. [34, 45-47, 54].
The CTEs of pure LZ are lower than that of YSZ (11×10-6 /K at 1000 oC) [10]. As a result,
the CTE difference between the LZ top coat and bond coat in LZ based TBC system is larger
than that between the YSZ top coat and the bond coat in YSZ TBCs. This is a disadvantage
for LZ in TBC applications because this may lead to a large volume change during thermal
cycling process. However, CTE values of the LZ based coating can be increased by doping
with selected rare earth element dopants. For example, Xiang et al. showed that the CTEs of
(La0.7Yb0.3)2(Zr0.7Ce0.3)2O7 and (La0.2Yb0.8)2(Zr0.7Ce0.3)2O7 were higher in the high-
temperature range (above 400 oC) than that of pure LZ [53]. Meanwhile, Cao and Zhang
suggested that using Ce (5~20 %) to dope into LZ to increase the CTE value [47, 55].
0
2
4
6
8
10
12
14
0 200 400 600 800 1000 1200 1400 1600
CT
E (
×10
-6/K
)
Temperature (K)
Exp. by Lehmann [34]
Exp. by Chen [46]
Exp. by Guo [45]
Exp. by Zhang [47]
Calc. by Feng [54]
21
6 Mechanical properties of lanthanum zirconate based coating
6.1 Elastic properties
Elastic properties include Young’s modulus (E), bulk modulus (K), and shear modulus (G).
These elastic properties can be measured by using the depth-sensing micro- and nano-
indentation technique or the ultrasound pulse-echo method [10, 18]. In the micro-indentation
technique, E can be obtained from the slope of unloading stress-strain curve by adopting
Sneddon’s flat-ended cylindrical punch model [10]. Shimamura et al. studied the moduli of a
series of Ln2Zr2O7 materials using the ultrasound pulse-echo measurement [18]. Shimamura
found that the elastic moduli (except for the Poisson’s ratio) strongly depend on the atomic
radius of rare earth elements in the lanthanide zirconate pyrochlore Ln2Zr2O7. A larger atomic
radius corresponds to higher E, K, and G values. La has a larger atomic radius than Nd, Sm
and Gd, so LZ has larger elastic modulus than Nd2Zr2O7, Sm2Zr2O7 and Gd2Zr2O7 [18].
Many researchers measured the elastic moduli of the LZ powder and coating, as
summarized in Table 2. The sample used in Vassen’s work was prepared by pressing La2Zr2O7
powders in the temperature range of1350~1400 oC. Zhang et al. measured APS deposited LZ
coating with a porosity of 7.53 % [26]. Xu et al. investigated E values of EB-PVD deposited
LZ coating [56]. Shimamura et al. used LZ powder samples and measured using the
ultrasound pulse-echo method [18]. Girolamo et al. tested APS deposited LZ coating, which
was exposed at 1350 oC for 50 h [28].
The Young’s moduli of hot pressed LZ sample are about 15% lower than that of the hot
pressed 8YSZ, which is ~ 210 ±10 GPa. The low Young’s moduli of LZ are advantageous for
reducing thermal stresses, which might compensate CTE mismatch in coatings [10].
6.2 Hardness and fracture toughness
Hardness test can be classified into three categories according to the length scale applied
in the measurement: macroindentation hardness, microindentation hardness, and
nanoindentation hardness. The measured hardness data of LZ coatings are listed in Table 2.
The samples used in each researcher’s work are the same as aforementioned in section 6.1.
22
The hardness of LZ varies significantly due to the sample density change. The hardness
increases with increasing coating density.
Fracture toughness (KIC) is a material property which describes the ability of fracture
resistance to maintain cracks in the material without crack propagation. The standard
measurement method of KIC is the four-point bending test of bulk samples. Another
alternative technique is the indentation method, which is widely used to evaluate the KIC
values of ceramic and coating systems [52]. The KIC values of LZ powders and coatings are
summarized in Table 2.
Hot pressed 8YSZ has higher hardness and KIC than LZ (microindentation hardness of
densified 8YSZ is 13±1 GPa, KIC of densified 8YSZ is 2.0-3.3 MPa·m1/2) [10, 57]. The low
KIC is the major disadvantage of LZ, which leads to a severe limit on its application as a TBC
material.
To improve the KIC of LZ material, a composite or multilayer LZ coating can be used.
Jiang et al. studied the microstructure and mechanical properties of LZ-Zr0.92Y0.08O1.96
composite ceramics, which were prepared by spark plasma sintering at 1450 oC. The results
revealed that the composite ceramics had a higher KIC than single phase LZ [58]. Jiang et al.
also showed that the KIC of composite LZ and 4YSZ coatings increased with increasing the
content of 4YSZ. The KIC reached to a value of 1.8±0.1 MPa m1/2 for 50% 4YSZ plus 50%
LZ composite coating, which is about two times of that of single phase La2Zr2O7 coating.
Guo et al. compared single LZ and double-layer LZ-8YSZ coatings [45]. The results
showed that the double-layer coating composed of LZ plus porous 8YSZ substantially
improved the durability in thermal cycling tests, suggesting the bi-layer design is a feasible
solution to improve the fracture toughness in LZ based coatings.
Table 2: Mechanical properties of LZ coating vs. YSZ coating
LZ YSZ
Young’s modulus
175±11 GPa (densified powder, Vassen [10])
156±10 GPa (coating, Zhang [26])
153 GPa (coating, Xu [56])
210 ±10 GPa
(densified powder,
Vassen [10])
23
280 GPa (powder, Shimamura [18])
141 GPa (porous coating, Girolamo [28])
Bulk modulus 216 GPa (Shimamura [18]) -
Shear modulus 109 GPa (Shimamura [18]) -
Poisson’s ratio 0.28 (Shimamura [18]) -
Vicker’s hardness 5.51 ± 0.25 GPa (coating, Zhang [26])
8.83 GPa (coating, Xu [56]) -
Microindentation
hardness 9.9 ± 0.4 GPa (densified powder, Vassen [10])
13±1 GPa
(densified powder,
Vassen [10])
Nanoindentation
hardness 8.8± 2.1 GPa (coating, Zhang [26]) -
Fracture toughness
1.1±0.2 MPa m1/2 (densified powder, Vassen [10])
1.84 MPa m1/2 (coating, Xu [56])
0.9 MPa m1/2 (densified powder, Jiang [58])
2.0-3.3 MPa·m1/2
(Beshish [57])
7 Thermal, mechanical, chemical and durability analyses
7.1 Thermal cycling test
Thermal cycling tests are applied to simulate the operation environment of TBCs in gas
turbines. Thermal cycling tests can be sorted into two broad categories based on temperature
gradient during thermal process [59]. (1) A constant temperature distribution in the sample
without a gradient in TBC samples. When heating/cooling rates are low, such as the furnace
cycling test (FCT), the sample is slowly heated in a furnace, which creates a high-temperature
isothermal environment for the entire TBC system, and then it is cooled by the compressed
gas or ambient air cooling out of the furnace [60]. (2) The thermal cycling tests with a
temperature gradient across the sample due to fast heating/cooling, such as the jet engine
thermal shock (JETS) test, laser rig and flame rig [59]. In the JETS test, a typical cycle consists
of a 20 s heating process, a 20 s forced nitrogen gas cooling and a 40 s dwell cooling in
ambient air environment. The front surface temperature can reach 1400 oC. The failure
24
criterion in the JETS tests is more than 20 % spallation of the TBC sample. Since the back
side of the sample is not heated, a thermal gradient is generated in the TBC samples during
the JETS test. The temperature gradient in the JETS over the whole sample depends on the
thickness of the coating system, coating composition, porosity, and microstructure of the
coating [60].
Although the maximum temperature and the heating and cooling duration time vary in
different thermal cycling tests, large thermal stress and strain mismatch generated due to the
CTE mismatch between the top and bond coats are the principal reason for the failure of LZ
coatings. To obtain a long thermal cycling lifetime, the LZ coating needs to accommodate the
thermal strain associated with thermal cycling [2]. In addition, oxidation of bond coat and low
KIC of LZ are additional factors for the spallation of the LZ coating [45, 61].
Many researchers have conducted thermal cycling tests of LZ in different testing
conditions. Because the TBC is a complicated system, the thermal cycling results vary due to
different cycling test parameters, coating porosities, coating microstructures, multilayer
coating architectures, and coating compositions, etc. Vassen et al. conducted thermal cycling
test with a large temperature gradient across the sample [10, 37, 62]. The APS deposited LZ
coating with single-layer coatings and the APS double-layer coatings with YSZ plus LZ top
coat were used in these tests. These TBC systems were tested in the surface temperature range
of 1200–1450 oC. The heating and cooling time periods were 5 min and 2 min. The results
indicated that the single-layer coating had a rather poor thermal cycling performance. The
double-layer system showed a similar to or slightly better performance than that of YSZ
coatings at temperatures below 1300°C, suggesting the double-layer coating with YSZ is an
effective way to improve the lifetime of TBC in thermal cycling tests [62]. Meanwhile, Cao
et al. also showed that the single-layer LZ coating had a short thermal cycling lifetime, but
the double-layer LZ coating with La2O3-ZrO2-CeO2 composite sublayer can greatly improve
the lifetime [63]. However, the more layers that the TBC coating has, the more artificial
defects might be generated during the deposition process. To reduce artificial defects, the
composition, thickness and porosity in the double-layer coatings need to be properly tailored.
Bobzin et al. investigated the thermal cycling performance of EB-PVD deposited LZ and
7YSZ coatings using the FCT test [61]. The samples were heated to 1050 oC for about 30 min,
25
then cooled to 35 oC in compressed air for 5 min. Delamination of the LZ coating occurred at
1856 cycles, which showed a better performance than 7YSZ coating (1380 cycles). The
alumina scale was observed in Bobzin’s thermal cycle experiments, which was evidence of
bond coat oxidation. Bobzin suggested that the main reason of the failure was a combined
effect of oxidation of the bond coat and CTE mismatch. Guo et al. conducted JETS test for
single-layer LZ coating and double-layer coating composed of LZ and 8YSZ deposited by
APS with different porosities [45]. The front surfaces of the TBC samples were heated to
1232 oC for 20 s, cooled by compressed N2 gas for 20 s and followed by ambient cooling for
40 s. The front and back side temperatures were monitored during the test by pyrometers to
analyze the cross-sectional temperature gradient. The initial spallation time of the TBC can
be pinpointed by the temperature difference between the front and back side surfaces. Guo et
al. showed that the single-layer porous 8YSZ coating had better JETS performance than the
single-layer porous LZ coating. Additionally, Guo et al. showed that the thermal durability of
LZ based coating can be improved by introducing a porous 8YSZ buffer layer between the
top and bond coat [45].
7.2 Erosion test
Erosion is regarded as a secondary cause of TBC failure by deteriorating the coating
through progressive removal of the coating material, due to the mechanical interaction
between coating surface and impinging solid particles [64]. The erosion tests by solid particle
impingement were standardized by ASTM G76-13 [65]. Typically, Al2O3 medium with a
particle size of 50 μm is used as the abrasive particles, and the abrasive particles are
accelerated by the high-velocity carrier gas through a particle-gas supply system. Finally, the
abrasive particles are impacted on the surface of the coating at a specific impinging angle.
The average erosion rate (mg/g or g/kg) is used to evaluate the erosion resistance performance,
which is determined by the slope of TBC mass loss (mg) versus the mass (g) of erodent curve.
Many variables like velocity, working distance, impact angle, abrasive particles properties,
coating hardness and mechanical properties of coating (H and KIC) can affect the erosion
results.
26
Erosion models of brittle materials such as the top coat in TBC can be described using the
indentation theory of abrasive particles, which focuses on the relationship between TBC’s
material properties (e.g., E and KIC) and the erosion process conditions (e.g., impact velocity
and abrasive particle size) [66-69]. It is necessary to determine whether an impinging particle
will initiate cracks in the target material. The velocity threshold is used to express the critical
condition to initiate the crack. Wellman proposed that the critical velocity of the abrasive
particles to initiate fracture can be given by [70]:
105⁄
⁄ ⁄ ⁄ (1)
where E is Young’s modulus, H is hardness, KIC is fracture toughness, ρ is the density of the
abrasive particles and R is the particle radius. Since LZ has a lower KIC than 8YSZ, low
erosion resistance of LZ in the erosion test is expected [71].
Ramachandran et al. studied the erosion of APS deposited YSZ and LZ coatings with
different coating porosities, abrasive particle velocities, and impact angles [72]. They found
that the porosity level is the most predominant factor affecting the erosion rate of the coatings.
High porosity in the coating increased erosion rate. The erosion rate increased with the
increasing of the abrasive particles’ velocity, which is consistent with Wellman’s model in
Equation 1. In addition, Ramachandran et al. found that LZ based coatings exhibited a better
erosion resistance than the YSZ coatings, which was different from the theoretical expectation
using Wellman’s model.
One method to improve the erosion resistance is to use microstructure modification. For
instance, columnar microstructure of EB-PVD deposited coating typically provides
improvement of erosive resistance compared to the “splat” grain microstructure of APS
deposited coating [64]. In addition, aging of APS coating decreases the erosion rate and
therefore enhances the erosion performance. However, the aging of EB-PVD coating results
in a significant increase of erosion rate due to the sintering of columns [64].
7.3 Hot corrosion and CMAS infiltration damage
During operation of a gas turbine engine, turbine ingests the intake air with various
airborne chemical substances which will be burned with the fuel and air. The operation
27
environment is filled with fuel, oxidized gasses and synthesized corrosive substances, which
may deteriorate the coatings and substrates, so the chemical stability is important for TBCs.
The most typical corrosive chemicals for TBCs in a gas turbine engine include vanadium
compounds (V2O5, NaVO3), sulfur-containing compounds (SO2 and sulfate salts such as
Na2SO4, MgSO4), and the mixture of them [73, 74]. When the APS deposited LZ based TBC
was exposed to the single corrosive chemical at high temperature, it was less damaged by the
vanadium compounds (at 1000 oC) but severely attacked by the sulfur-containing compounds
(at 900 oC). However, the performance of the APS deposited 8YSZ based TBC in the same
test was just the opposite situation. In the vanadia environment, many micro-cracks were
generated in the 8YSZ coating, and spallation occurred finally. However, the 8YSZ coating
showed an excellent resistance to sulfur-containing compounds [73]. In expecting to improve
the corrosive resistance from Na2SO4 and V2O5, the LZ coating was deposited using EB-PVD
with the addition of Y2O3 [74]. The composited coating exhibited a good resistance to V2O5
but experienced severe damage in the mixture of Na2SO4 + V2O5. Xu et al. indicated that the
excess of La2O3 in the composited coating can aggravate the corrosion by Na2SO4 and V2O5
[74].
The degradation of TBC by molten calcium–magnesium–alumino-silicates (CMAS) and
volcanic ash infiltration have been concerned since TBC was introduced in gas turbines [75,
76]. CMAS attack primarily affects high-performance jet engines on account of their higher
maximum temperatures and electricity-generation engines in some locations, but it will likely
affect more engines as operation temperatures are increased in pursuit of greater engine
efficiencies [77]. In the case of land-based electricity-generation engines, it is not always
practical to filter out the finest particles that can be carried along with the input air and from
alternative fuels such as syngas [77]. CMAS debris and the volcanic ashes are usually ingested
with the intake air and deposited on TBCs. At elevated temperatures, the debris becomes
liquid and penetrates the open void space in the coating. During the cooling process, it
solidifies and reduces the strain tolerance of the coating [78]. When CMAS infiltration occurs
in TBCs, a thermal shock delamination mechanism is easily activated [76]. Drexler et al.
showed that TBCs with a good resistance against the CMAS must have a vigorously
interaction with the molten CMAS, which result in rapid crystallization of the refractory oxide
phase that form a sealing layer, stopping further penetration of the molten CMAS [79]. Rare
28
earth pyrochlore materials, such as Ga2Zr2O7 and La2Zr2O7 were found to be highly effective
in resisting high-temperature penetration of the molten CMAS debris and volcanic ash for
prolonged durations[80-83]. This resistance is attributed to the formation of a sealing layer
made of crystalline Ca-apatite phase (Ca2Gd8(SiO4)6O2 and Ca2La8(SiO4)6O2) which prevents
further infiltration of the liquid CMAS into the TBC[80, 83]. The CMAS resistance
mechanism works for both APS and EB-PVD La2Zr2O7 coatings. Comparing to La2Zr2O7,
YSZ coating is easily to be deteriorated by CMAS owing to (1) CMAS’ potential for de-
stabilization of the metastable tetragonal phase (t’-YSZ), and (2) CMAS’ penetration through
the cracks of APS coating and the inter-columnar gaps of EB-PVD coating and reach far away
to the TGO layer[75]. Because YSZ coating is lack of rapid formation of the crystalline
products, it is vulnerable to CMAS attack or volcanic ash[83].
8 Modeling and simulation
8.1 Thermal property calculations
Material properties, including the physical, thermal and mechanical properties, can be
calculated using modeling methods, such as first principles calculations, molecular dynamics
(MD) method, finite element (FE) method, etc.
Feng et al. calculated the CTEs for Ln2Zr2O7 (Ln= La, Nd, Sm, and Gd) using the first
principles calculations, as shown in Fig. 10 [54]. The quasi-harmonic approximation (QHA),
Debye approximation and density functional theory (DFT) were employed in Feng’s work to
calculate the CTE as a function of temperature. The CTE (α, β) can be calculated using [54]:
(2)
where Cp and Cv are the specific heats at constant pressure and volume, respectively; β is the
volumetric CTEs, 3 ; α is the linear CTEs, T is the temperature, and B0 is the isothermal
bulk modulus. The calculated CTE results showed good agreement with other researcher’s
experimental data [54]. Guo et al. investigated the Cp of LZ single crystal using the first
principles calculations, as shown in Fig. 8 [48].
29
The MD method can be used to investigate the thermal conductivity. For single crystals,
there are two common molecular dynamics methods for thermal conductivity calculations,
i.e., direct method [84, 85] and Green-Kubo method [86, 87]. The direct method is a non-
equilibrium molecular dynamics (NEMD) method which imposes a temperature gradient to
the system. The Green-Kubo method is an equilibrium MD (EMD) method which uses the
current fluctuation to calculate the thermal conductivity according to the fluctuation-
dissipation theorem [88]. Schelling et al. predicted the thermal conductivities of several
dozens of single crystal pyrochlores with the composition of A2B2O7 (A is a rare earth element,
and B=Ti, Mo, Sn, Zr or Pb) using the NEMD methods with Buckingham potentials [84]. The
calculated thermal conductivity of single crystal LZ was 1.98 W/m/K at 1200 oC [84]. A more
reliable method to compute thermal conductivity is the reverse NEMD (RNEMD) method
[89]. In RNEMD method, the Muller-Plathe algorithm [90] is used to exchange kinetic energy
between two atoms in different regions of the simulation box at every finite step to induce a
temperature gradient in the system. It works by exchanging velocities between two atoms in
different parts of the simulation cell. At set intervals, the velocity of the fastest atom in one
region is replaced by the velocity of the slowest atom in another region and vice versa.
Consequently, the first region becomes colder, whereas, the second region increases in
temperature. The system will be reacted by flowing energy from the hot to cold regions.
Eventually, a steady state is established when the exchanged energy equilibrates the energy
flowing back in a temperature gradient over the space between. The usual NEMD approach
is to impose a temperature gradient on the system and measure the response as the resulting
heat flux. In RNEMD using the Muller-Plathe algorithm, the heat flux is imposed, and the
temperature gradient is the system’s response. The advantage of NEMD over traditional
NEMD is that there are no artificial ‘‘temperature walls’’ in the simulated system, since these
cause a fluid structure different from the bulk. Additionally, energy and momentum are
conserved, and there are no thermostat issues [89].
Chartier calculated the Cp of LZ using molecular dynamic (MD), as shown in Fig. 8 [49].
The Buckingham and Coulomb force field was used to describe the interaction between each
atom. As shown in Fig. 8, the predicted Cp values were very close to the experiments result.
Schelling et al. investigated the thermal conductivity of pyrochlores with the composition of
A2B2O7 (A=La, Pr, Nd, Sm, Eu, Gd, Y, Er or Lu; B=Ti, Mo, Sn, Zr or Pb) using molecular
30
dynamics method at 1200 oC [84]. The results showed that the thermal conductivities did not
show a strong dependence on ionic radius of A, but tended to decrease with increasing ionic
radius of B, as shown in Fig. 11 [84].
Fig. 11: Contour map of thermal conductivity of A2B2O7 as a function of radii of A and B ions [84].
The FE method has been used to simulate heat conduction process of coating structures
with cracks and pores [91]. In addition, the quantitative imaging analysis method can be used
to investigate the non-uniformity properties of the porous coating with polycrystalline
microstructure [26, 40]. The pore and crack morphology of TBC is an important parameter
affecting the mechanical and thermal properties [92, 93]. The thermal properties of non-
uniform porous polycrystalline coatings can be calculated using image based FE method.
Image based FE method uses scanning electron microscope (SEM) images to generate
microstructures and import into the FE model [94].
Arai et al. studied the thermal conductivities of TBCs with different porosities using SEM-
image-based FE modeling [93]. They found that the presence of the pores disturbed the heat
31
transfer in their models. In addition, the thermal conductivity of plasma sprayed porous YSZ
was investigated by many researchers using FE method [95, 96]. The calculated effective
thermal conductivities were in good agreement with experimental results. Guo et al. predicted
the thermal conductivity of porous LZ coatings using an image based multi-scale simulation
method, which combined the MD and FE calculations[51]. The reverse non-equilibrium
molecular dynamics approach was used in Guo’s work to compute the temperature-dependent
thermal conductivity of single crystal LZ. The single crystal thermal conductivity values were
then passed to the FE model which was generated from the SEM images of the LZ coating
with a porosity of 10.0 % ~12.3%. The predicted thermal conductivities from the FE model
are shown in Fig. 9. The imaged based FE calculated thermal conductivity data are slightly
lower than the experiments data. The deviation might come from the artificial errors during
the SEM image conversion and the FE mesh process. The limitation of this image based FE
model is that SEM images can’t fully reflect the coating microstructure in 3-dimensional
space. The model converted from the SEM images might miss some microstructure details,
which leads to the deviation of the thermal conductivity results.
8.2 Mechanical property calculations
Similar to aforementioned thermal properties, the mechanical properties of LZ crystal can
also be predicted using various modeling techniques.
The elastic constants of a material describe its response to an applied stress or, conversely,
the stress required to maintain a given deformation. Elastic properties such as Young’
modulus, bulk modulus, shear modulus and Poisson’s ratio can be analytically calculated from
the elastic constants [97]. Liu et al. calculated the elastic constants of LZ using the first
principles calculations [98]. From the results of elastic constants, Liu calculated the
anisotropic E values on (011) plane. The maximum Young’s modulus was 225 GPa, which
was along <111> direction. The minimum Young’s modulus was 214 GPa, which was along
<100> direction [98]. Feng et al. investigated the hardness and elastic modulus using local-
density approximation of spin polarized scheme (LDA+U, U is Hubbard energy) [99]. The
calculated bulk modulus was 176 GPa, Young’s modulus was 208 GPa, shear modulus was
87 GPa, Poisson’s ratio was 0.302, and the calculated hardness was 8.9 GPa. The theoretically
32
calculated results are in good agreement with experimental results, which are listed in Table
2. Again, there are some deviations between the modeling and the experimental results,
because the models used in the above calculations are for perfect crystal. The actual samples
contains grain boundaries or defects.
8.3 Gas adsorption and oxidation modeling
Complementing to experimental effort, modeling technique provides an alternative way to
interpret gas adsorption and oxidation process. Oxidizing gas adsorption on TBC surface is
the first step of the oxidation process. The surface energies on (001), (011) and (111) planes
in LZ need to be calculated, before the calculated the gas adsorption. Guo et al. studied the
CO2 and O2 molecule adsorption on the surface of LZ using the DFT method [100, 101]. The
(011) plane was the most thermodynamically stable planes in LZ crystal. The plane with the
lowest adsorption energy was regarded as the most favorable gas adsorption plane.
Oxygen migration in TBCs results in the oxidation of the bond coat to form the TGO layer,
which may protect the bond coat from rapid oxidation if a slow growing alpha alumina scale
is formed. However, if the oxygen migration continues, the TGO layer grows thicker. This
can also lead to the delamination of TBCs due to crack generations in thick TGO layer. Pirzada
et al. predicted the activation energies for the oxygen migration using the atomic scale
simulation [102]. In this model, the oxygen migration proceeded through an oxygen vacancy
mechanism with the oxygen ions hopping between 48f sites and the unoccupied 8a interstitial
position played an important role in the migration mechanism. The oxygen migration
activation energy was calculated for a series of A2B2O7 materials (A= La, Pr, Nd, Sm, Eu, Gd,
Y, Er, Yb, Lu and B=Ti, Ru, Mo, Sn, Zr,Pb), as shown in Fig. 12 [102]. The results suggest
that the activation energies may not be strictly related to the radii of the A and B cations. LZ
crystal exhibits a higher activation energy for oxygen migration than other zirconate
pyrochlore compounds containing rare earth elements which may minimize the chance of
oxidation failure in TBCs.
33
Fig. 12: Oxygen migration activation energy of A2B2O7 materials as a function of radii of A and B cations [102]
9 Concluding remarks on future research directions
In this paper, lanthanum zirconate material and its application as thermal barrier coating
are comprehensively reviewed. The coating deposition technique, the physical, thermal,
mechanical, and thermal durability of the coatings are summarized. In general, LZ coatings
have much better thermal and phase stability than 8YSZ coatings. The hardness of LZ coating
is slightly lower than that of 8YSZ, and the fracture toughness is much lower than that of
8YSZ. Since TBC is a quite complicated composite material system, there are many factors
related to the TBCs properties and durability, the research on LZ based TBC is still far from
the end. Based on this review, the following research directions are identified for LZ to be
used as promising TBC materials.
(1) LZ coating has a lower fracture toughness than 8YSZ, as shown in Table 2. The low
fracture toughness leads to cracking at modest stress levels. It becomes very important to
34
improve the fracture toughness of LZ based coatings. Strategies include composite coating
or multi-layer gradient coating architectures, which have demonstrated improved
durability performance in thermal cycling test. The exact composite or multi-layer
structures need to be optimized since artificial defects may be introduced at the interface.
Another strategy could be using doping of LZ, which shows increased fracture toughness.
Again, the selections of doping elements and the doping ratio are still unclear, which
requires further investigation.
(2) The coefficient of thermal expansion of LZ needs to be increased to minimize residual
stress at the interface between the top and bond or substrate. Using doping with selected
elements, coefficient of thermal expansion can be slightly increased. However, a material
that has better thermal properties does not guarantee a good thermal cycling performance.
Thermal durability experiments of low thermal conductivity materials need to be
conducted to simulate gas turbine operating conditions.
(3) Further studies of hot corrosion and CMAS resistance of LZ material are needed, as the
operating environments of advanced gas turbines contains multiple chemicals and
substances, which will affect the chemical stability at extreme conditions.
(4) Failure mechanisms of LZ coatings in combined thermal, mechanical, and chemical
environment are totally unclear. The integration of experimental techniques and
theoretical modeling tools can be the most powerful way to unfold the mystery of failures
in the LZ based TBCs. The modeling studies of interfacial failure, TGO initiation and
growth, bond coating oxidation and cracking in LZ coating are still challenging, which
are needed to fully understand failure mechanisms and improve the design of future
advanced TBC coatings.
Acknowledgments
Jing Zhang acknowledges the financial support provided by the United States Department
of Energy (Grant No. DE-FE0008868, program manager: Richard Dunst) and IUPUI RSFG
35
and IDRF grants. Jing Zhang thanks Yang Ren at Argonne National Laboratory for generating
the synchrotron XRD data shown in Fig. 4, through using the resources of the Advanced
Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated
for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-
AC02-06CH11357. Yeon-Gil Jung acknowledges the financial support provided by the
National Research Foundation of Korea (NRF) Grant funded by the Korean Government
(MEST) (2011–0030058), by the Power Generation & Electricity Delivery of the Korea
Institute of Energy Technology Evaluation and Planning (KETEP) Grants funded by the
Korea Ministry of Knowledge Economy (2013-101010-170C). The authors also thank the
critical comments from the anonymous reviewers.
36
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